Numeracy Information Session 1 How kids work mathematically? Knowing the language of maths

Australian Curriculum Numeracy Learning Continuum The Numeracy learning continuum is organised into six interrelated elements: Estimating and calculating with whole numbers Recognising and using patterns and relationships Using fractions, decimals, percentages, ratios and rates Using spatial reasoning Interpreting statistical information Using measurement These elements are drawn from the strands of the Australian Curriculum: Mathematics as shown in the table

Numeracy Learning Continuum Years P–2 (typically from 5 to 8 years of age) Children in the early years have the opportunity to access mathematical ideas by developing, a sense of number, order, sequence and pattern; understandings of quantities and their representations, and attributes of objects and collections, and position, movement and direction; and an awareness of the collection, presentation and variation of data and a capacity to make predictions about chance events. Developing these understandings and the experiences in the early years provides a foundation for algebraic, statistical and multiplicative thinking that will develop in later years. These aspects of early mathematics build the foundations with which children can pose basic mathematical questions about their world, identify simple strategies to investigate solutions, and strengthen their reasoning to solve personally meaningful problems.

Numeracy Learning Continuum Years 3–7 (typically from 8 to 12 years of age) The curriculum will develop key understandings for these years by: extending the number, measurement, geometric and statistical learning from the early years; building foundations for future studies by emphasising patterns that lead to generalisations describing relationships from data collected and represented, to make predictions; and introducing topics that represent a key challenge in these years such as fractions and decimals. Particularly in these years of schooling, it is important for students to develop deep understanding of whole numbers to build reasoning in fractions and decimals and develop their conceptual understanding of place value. With these understandings, students are able to develop proportional reasoning and flexibility with number through mental computation skills. These understandings extend students’ number sense and statistical fluency.

What has changed in the teaching of maths? There may be nothing as certain as a number, but the way children are taught to handle them has changed. As any parent of a primary age child knows, pupils come home with an array of new strategies in their homework books and terms in their brains to help them tackle their maths homework. Number lines and number grids have replaced counting on your hands, and perplexing terms like chunking and partitioning represent the new ways of tackling arithmetic in schools. Modern maths teaching focuses on the key concepts, and a renewed emphasis on mental methods and strategies as opposed to recall. http://www.schoolatoz.nsw.edu.au/homework-and-study/mathematics/mathematics-tips/helping-your-child-with-maths

Rainbow Number Facts The “Rainbow Facts” are pairs of numbers whose sum is 10. These facts form the basis of counting and mental computation in the early years. Ten is the basis of our number system so we teach children the number combinations that add up to 10.

Ten Frames An empty chart that has 2 rows of 5. This frame helps children to visualise the numbers 1 to 10. http://www.schoolatoz.nsw.edu.au/homework-and-study/maths/maths-a-to-z/-/maths_glossary/RId5/231/ten+frame

Partitioning? Partitioning is a way of working out maths problems that involve large numbers by splitting them into smaller units so they’re easier to work with. So, instead of adding numbers in a column, like this… 79 + 34 113 …younger students will first be taught to separate each of these numbers into units, like this… 70 + 9 + 30 + 4 …and they can add these smaller parts together. For instance, they can pick out all the tens and work down to single units, making the problem more and more manageable, like this… (70 + 30) + (9 + 4) = 100 + 13 = 113

Why are children taught partitioning? Children are taught this method before they learn to add numbers in columns. Partitioning gives children a different way of visualising maths problems, and helps them work out large sums in their head. By breaking numbers down into units that are easy for them (and us!) to calculate mentally, they can reach the correct answer without counting out tricky double or triple-digit numbers on their fingers or trying to remember where a decimal point needs to be. When do children start to partition numbers? Partitioning is taught in Year 1, to make children aware that a two-digit number is made up of tens and ones.

Partitioning in addition These are two commonly used methods for adding larger numbers: A teacher might start teaching children to add two-digit and three-digit numbers in Year 3 by partitioning. The reason for this is that it helps children to mentally add multiples of ten (70 + 50 for example) and multiples of 100 (400 + 800 for example). Children in Year 3 should also learn to add three-digit numbers using the column method, so your child is likely to encounter both of these methods.

Partitioning in multiplication & division Children in Year 3 will also need to multiply two-digit numbers by a one-digit number. They will usually be taught this by partitioning, for example: 37 x 4 = 30 x 4 = 120 7 x 4 = 28 120 + 28 = 148 As children move into Year 4 and 5, they have to start multiplying two two-digit numbers. There are two commonly used methods for this (the grid and column methods); the grid method uses partitioning The grid method is used so that children are repeatedly practising multiplying multiples of ten with other numbers, for example: 30 x 20, 30 x 3, 20 x 8, etc. Once teachers are very confident that a child is aware of how to multiply multiples of ten and one hundred, they will often allow a child to move onto the quicker column method. Children will also need to divide two-digit numbers by a one-digit number. They will using be taught this by partitioning using a chunking method. http://www.bbc.com/news/education-18147368

Jump strategy on a number line – Strategies students are taught in solving addition and subtraction problems Students use and record a range of mental strategies to solve addition and subtraction problems involving two-digit numbers, including: Jump strategy on a number line – an addition or subtraction strategy in which the student places the first number on an empty number line and then counts forward or backwards, first by tens and then by ones, to perform a calculation. (The number of jumps will reduce with increased understanding.) http://www.schoolatoz.nsw.edu.au/homework-and-study/maths/maths-a-to-z/-/maths_glossary/RId5/130/jump%20strategy

Split strategy An addition or subtraction strategy in which the student separates the tens from the units and adds or subtracts each separately before combining to obtain the final answer. Split strategy method:  eg 46 + 33      http://www.schoolatoz.nsw.edu.au/homework-and-study/maths/maths-a-to-z/-/maths_glossary/RId5/218/split+strategy

Compensation Strategy Example                                                                                                                                                               Compensation Strategy The compensation strategy is to assist students in addition of two digit number or greater. One number is rounded to simplify the calculation then the answer is adjusted to compensate for the original change. Example http://www.schoolatoz.nsw.edu.au/homework-and-study/maths/maths-a-to-z/-/maths_glossary/RId5/70/compensation%20strategy

Language of Fractions

Adding or subtracting fractions Example: 𝟒 𝟓 + 𝟐 𝟑 Rule of thumb: Cannot add fractions that have different denominators. Must convert fractions to equivalent fractions in order to add fractions When converting fractions you multiply the denominator by a number. Whatever you have done to the bottom you must do to the top?

The language of Mathematics A whole number A whole number is a non-negative integer, that is, one of the numbers 0, 1, 2, 3, … Sometimes it is taken to mean only a positive integer, or any integer. An Integer a number which is not a fraction; a whole number. includes the counting numbers {1, 2, 3, . ..}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...} A numeral A figure or symbol used to represent a number. For example, –3, 0, 45, IX.

Place value Partitioning The value of a digit as determined by its position in a number relative to the ones (or units) place. For integers the ones place is occupied by the rightmost digit in the number. For example, in the number 2594 the 4 denotes 4 ones, the 9 denotes 90 ones or 9 tens, the 5 denotes 500 ones or 5 hundreds, the 2 denotes 2000 ones or 2 thousands, Partitioning Dividing a quantity into parts. In the early years it commonly refers to the ability to think about numbers as made up of two parts, for example, 10 is 8 and 2. In later years it refers to dividing both continuous and discrete quantities into equal parts ie fractions, decimals, ration.

Multiple A multiple of a number is the product of that number and an integer. A multiple of a real number x is any number that is a product of x and an integer. For example, 4.5 and –13.5 are multiples of 1.5 because 4.5=3×1.5  and −13.5=−9×1.5  Factor A number or quantity that when multiplied with another produces a given number or expression. Highest common factor The highest common factor (HCF), greatest common factor (GCF) or greatest common divisor (GCD) of a given set of natural numbers is the common divisor of the set that is greater than each of the other common divisors. For example, 1, 2, 3 and 6 are the common factors of 24, 54 and 66 and 6 is the greatest common divisor.

An array is an ordered collection of objects or numbers. A prime number is a natural number greater than 1 that has no factor other than 1 and itself example 11. A composite number A natural number that has a factor other than 1 and itself is a composite number A triangular number A triangular number is the number of dots required to make a triangular array of dots in which the top row consists of just one dot, and each of the other rows contains one more dot than the row above it. So the first triangular number is 1, the second is 3 (= 1 + 2), the third is 6 (= 1 + 2 + 3) and so on. An array An array is an ordered collection of objects or numbers.

Resources http://www.melmaria.wa.edu.au/parentguide.pdf http://www.hfluddenham.catholic.edu.au/SiteData/180/UserFiles/PublicationLinks/PARENT%20HANDOUT.pdf http://www.australiancurriculum.edu.au/mathematics/Curriculum/F-10?layout=1 http://www.math.com/ http://www.schoolatoz.nsw.edu.au/homework-and-study/mathematics/mathematics-tips/helping-your-child-with-maths http://www.currumbiss.eq.edu.au/Restricted/Currumbin%20numeracy/MentalComp.pdf